Thoughts? Im assuming the embroidery will "leak" for lack of a better term.
Yes and no.
If just do straight embroidery with no post embroidery treatment, then your odds of leakage are very very high.
If you do post treatment and seal those needle punctures then that should provide some protection.
It's not 100% effective, especially depending on how well the post treatment is applied, so there is always that caveat to that, but there is a method to help the fabric recover from the embroidery process.
Personally, depending on the logo, size and density, all the way around, it might be best to do some type of printer application or if they want the embroidery option, to do it as a patch if it's really stitch heavy.